The homeless man who allegedly shoved an off-duty NYPD cop onto Manhattan subway tracks late Tuesday is a career criminal who was recently cut loose on supervision after randomly slugging someone else on the rails, cops and prosecutors said.

Aaron Walker, 28 – who has 18 prior arrests – had only been out of cuffs for two days when cops say he hurled the 24-year-old officer onto the downtown roadbed at the Third Avenue L station in the East Village shortly before 7:30 p.m., sending him to the hospital.

Walker was picked up by police a short time later and now faces a top charge of attempted murder, authorities said.

His arrest came on the heels of a Saturday arrest for a local law violation, after officers spotted him smoking a cigarette on board a train at Bedford Avenue and North 7th

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